LANDOVER, Md. — The deficit was 7-0 far too quickly but then, Justin Tuck said, he believed the Giants had “kind of weathered that storm.’’ But then it got worse.

“At 14-0 you’re kind of like ‘Ugh,’ ’’ Tuck said.

Given where they have been, trailing 14-0 Sunday night to the Redskins, on the road at FedEx Field, put the Giants teetering on the edge of cashing in the game and perhaps the remainder of this disappointing season.

“I don’t think we could have quit,’’ Tuck said. “I don’t think we have quit in us.’’

The Giants did not cave in. Instead, they steadied themselves and staved off any further embarrassment by rallying for a 24-17 victory that was secured only after safety Will Hill yanked the ball out of the grasp of Pierre Garcon with 1:21 remaining to kill off the final Redskins drive.

“What I’m most proud of is the way we hung in there,’’ coach Tom Coughlin said.

Andre Brown rushed for two touchdowns and Tuck led a solid defensive charge with a career-high four sacks of Robert Griffin III as the Giants (5-7) won for the fifth time in their last six games. But they hardly showed much in the way of dominance over the Redskins (3-9) who, mercifully, are eliminated from the playoffs .

The Giants aren’t there yet, but they’re close. After last week’s agonizing last-second loss to the Cowboys, the Giants knew their playoff hopes were on life support. Those hopes were all-but expired by the time the Giants hit the field. The Cowboys took care of business by beating the Raiders on Thanksgiving and the Eagles earlier Sunday continued to roll by defeating the Cardinals. The Giants remain two games behind both the Cowboys and Eagles with four to play and do not own the tiebreaker on either opponent. The Giants need to win their final four games and, basically, hope the two teams in front of them collapse.

“We put ourselves in the situation we’re in,’’ Brown said. “We have to continue to win football games and hope for a miracle.’’

The last time the Giants and Redskins squared off was exactly one year ago and the circumstances for that prime-time clash could not have been more different. The Giants were in first place, the Redskins were gearing up for a sensational closing run and Griffin was the hot rookie quarterback prodigy.

A year later, this prime-time affair featured two teams going nowhere, out of playoff contention. The Redskins came out in a no-huddle offense, marched down the field and scored on Alfred Morris’ 1-yard touchdown plunge. Griffin completed his first 12 passes and the Redskins went ahead 14-0 early in the second quarter on a 19-yard scoring pass to tight end Logan Paulsen.

The Giants pulled within 14-7 by sticking to the ground and pounding away, first with Peyton Hillis on a 27-yard run and then Brown galloping 23 yards into the end zone, aided by big blocks from Kevin Boothe and Justin Pugh. Just 35 seconds before halftime, Eli Manning’s play-fake to Hillis caused cornerback E.J. Biggers to take a step towards the line of scrimmage, meaning he was lost in space as tight end Brandon Myers ran free over the middle for a 19-yard scoring pass play to make it 14-14.

Manning’s third-quarter pass sailed too high for Rueben Randle, the ball was deflected into the air by Washington cornerback David Amerson and intercepted by safety Brandon Meriweather, whose 32-yard return put the Skins on the Giants 12-yard line. Manning was bailed out when his defense limited the damage to a 33-yard Kai Forbath field goal.

A bad snap and a punt deflected by Damontre Moore put the Giants on the Redskins 46-yard line and passes of 18 yards to Myers and 19 yards to Victor Cruz set up Brown’s second rushing touchdown of the night. That put the Giants ahead 21-17, gaining a lead for the first time.

After the rough start, the Giants turned up the heat on defense. RG3 ran for 88 yards but the Giants were more concerned with Morris and they stopped him cold (11 carries, 26 yards). The Skins had a final shot but there was confusion with the chain gang and referee Jeff Triplette on what down it was, irking Redskins coach Mike Shanahan before Hill swiped the ball from Garcon.

“We played hard last week and didn’t get a win,’’ Coughlin said, “so they truly did show what they were made of.’’